# Journal of the Ramanujan Mathematical Society

Volume 36, Issue 3, September 2021 pp. 221–229.

Hodge locus and Brill-Noether type locus

**Authors**:
Indranil Biswas and Ananyo Dan

**Author institution:**School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India

**Summary: **
The aim in this article is to study effective Cartier divisors D
in a smooth projective variety X that satisfy the property that
for any infinitesimal deformation X{t} of X, the divisor D
lifts to an effective Cartier divisor on X{t} if and only if the
cohomology class of the divisor D lifts to a Hodge class. This
question is related to a classical problem in variational Hodge
theory and partially answered by Bloch in [1]. We answer the
question in terms of a Brill-Noether type locus associated to the
invertible sheaf corresponding to the divisor.

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